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Journal of the London Mathematical Society Advance Access originally published online on April 19, 2008
Journal of the London Mathematical Society 2008 78(1):125-142; doi:10.1112/jlms/jdn015
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© 2008 London Mathematical Society

Krull–Gabriel dimension and the model-theoretic complexity of the category of modules over group rings of finite groups

Gena Puninski

Department of Mathematics
University of Manchester
Lamb Building
Booth Street East
Manchester
M13 9PL
United Kingdom
gpuninski@maths.man.ac.uk

Vera Puninskaya and Carlo Toffalori

Department of Mathematics and Informatics
University di Camerino
Via Madonna delle Carceri 9
62032 Camerino
Italy
carlo.toffalori@unicam.it

We classify group rings of finite groups over a field F according to the model-theoretic complexity of the category of their modules. For instance, we prove that, if F contains a primitive cubic root of 1, then the Krull–Gabriel dimension of such rings is 0, 2, or undefined.

2000 Mathematics Subject Classification 16D50, 16S34, 16G30.

The research of the first author is partially supported by NFS Grant DMS-0612720.

Received May 30, 2006; revised September 25, 2007; published online April 19, 2008.


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